System and Method for Conducting a Recurring Auction Using a Participant Retention Mechanism

ABSTRACT

The present invention includes a method and system for trading goods and services through recurring auctions. Recurring auctions are increasingly popular form of markets for perishable and time-sensitive resources. Traditional auctions strive to motivate bidders to bid their true valuation of the resources traded. Yet, when successful, they also quickly divide the recurring auction bidders into permanent winners and permanent losers. The latter have no incentive to stay in the market, so they leave, decreasing the competitive pressure and depressing pricing. The present invention introduces a novel winner selection method to maintain customers&#39; interest in auction participation that employs participant retention mechanism in assigning traded resources to bidders. The winners are selected from a wider range of bidder ranks than in traditional auction mechanisms. For a group of bidders, winner selection takes into account bid values, and winnings and participation of each bidder in the previous auction rounds.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of application U.S. Ser. No. 11/258,476 filed Oct. 25, 2005, now U.S. Pat. No. 8,719,141 issued May 6, 2014. Said U.S. Ser. No. 11/258,476 in turn claims benefit of provisional application U.S. 60/622,028 filed Oct. 26, 2004. All of the foregoing are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to conducting commercial transactions, and more particularly, to conducting computerized recurring auctions comprising auction rounds allocating limited resources to competing bidders. Specifically, this invention relates to a computerized allocation procedure within a recurring auction. The procedure of this invention can be used in any general management application in which an allocation of physical resources, contracts, leases or operations to some of many competing bidders is made repeatedly.

2. Description of the Related Art

An auction is a market institution with an explicit set of rules matching supplies with demands for traded resources and determining sell prices on the basis of bids from the market participants [1]. In relation to the present invention, resources include goods, services, leases, licenses, contracts, orders, or anything else which auction participants are willing to trade. In many cases, auctions will repeat frequently, either to trade a new supply of consumable resources, or to trade a new period of time for reusable resources or for other relevant reasons.

For direct auctions, purchasers are termed bidders, and the seller or sellers are termed the auctioneer. For reverse auctions, the purchasers are termed the auctioneer and sellers are termed bidders. The present invention applies irrespective of whether the participants (bidders and auctioneers) carry out their roles directly, through an agent, or using an automated program, and also irrespective of whether the participants (bidders and auctioneers) are individuals, legal entities, or syndicates of individuals or legal entities. Also, for the purposes of this document a “higher” bid is defined as one more advantageous to the auctioneer, i.e., a higher bid for purchasing a resource in direct auctions and a lower bid for selling a resource in reverse auctions.

Participants' bids are dependent on their respective resource valuation that may vary widely across participants. When offered the resource at the price equal to his valuation, the bidder is indifferent between trading and not trading the resource. For each bidder, such valuation is called the true valuation of that bidder for the traded resource. The difference between the true valuation and the price paid for the resource defines the bidder's utility from a transaction[2]. On the other hand, the price paid by each winning bidder defines the revenue of the auctioneer. As a result, the total utility of an auction, that is the sum of the utilities of all bidders and the revenue of the auctioneer, is equal to the sum of the true valuations of the auction-winning bidders. Hence, one desirable property of an auction is allocating each resource to the bidder who values it the most (i.e., has the highest true valuation for this resource). This property ensures the highest possible total utility of an auction resulting in the so-called efficient auction[2]. Another important property, often related to the previous one, is to provide the incentive for the bidders to bid their true valuation, because if they do, making auction efficient is easy since the auctioneer knows the bidders true valuations from their bids.

By definition[2], the dominant strategy of each bidder is the strategy of selecting the bid that maximizes the bidder's utility from the auction. An auction mechanism that makes bidding true valuation the dominant strategy of each bidder is called incentive compatible. This is a desirable property for the auction mechanism as it enables an efficient auction and aims at maximizing the seller's revenue.

The bids entered in an auction could be either sealed (in which case, each bid is known only to the bidder issuing it and the auctioneer) or open, (in which case all bids are known to all bidders and the auctioneer). Common forms of sealed bid auctions include the First Price Sealed Bid (FPSB) auction and Second Price Sealed Bid (SPSB) auction.

In a First Price Sealed Bid (FPSB) auction, each bidder submits one sealed bid (in ignorance of all other bids) to the auctioneer. The latter determines the highest bid; the bidder with this bid receives the resource at the price equal to his bid (so in a basic FPSB auction the bid value is equal to the bid).

In a Second Price Sealed Bid (SPSB) auction, each bidder also submits one sealed bid and the bidder with the highest bid is the winner. However, the selected winner pays the price that is equal to the second-highest bid. This auction mechanism is also called the Vickrey Auction[3]. Vickery proved theoretically that the dominant strategy for each bidder is to bid his true valuation[3].

The basic auction mechanisms described above have been generalized in many directions. In a Multi-attribute Auction (MA), the auctioneer selects winners based on a bid as well as on various other attributes, some of which may be a component of the bid (such as a proposed settlement time), while others may be properties of the bidder. A generic procedure for selecting winners in a multi-attribute auction in electronic procurement environments is presented in [4]. The utility function of a Multi-attribute Auction is based on Multi-Attribute Utility Theory (MAUT) [4].

Combinatorial Auctions allow each bidder to offer a bid for a collection of goods (of the bidder's choosing) rather than placing a bid on each resource separately. This enables the bidder to express dependencies and complementarities between goods. The auctioneer selects such set of these combinatorial bids that result in the largest revenue without assigning any object to more than one bidder. However, determining the set of winners of the auction that maximizes the revenue for large numbers of bids is computationally very intensive (more precisely, it is an NP-complete problem [5]). Under certain restrictions, such as a limited number of bids, an efficient solution is possible [6]. An auction house with a generalized combinatorial auction is described in [7].

The Vickrey Auction has also been generalized to the case in which there are multiple units of a resource [8]. The so-called Generalized Vickrey Auction (GVA) mechanism determines the allocation of multiple units of a resource to the bidders in a way that makes the auction incentive compatible but finding such allocation is computationally intense (NP-complete [8]).

In the current state of the art, all auction systems can be generalized into the six-step process as described below and depicted in FIG. 1.

The bid collection and validation procedure collects the bids from the users participating in the market. This component can be represented by a human agent or can be embedded in a computer system. Bids may be firm (not revisable or cancelable) or changeable under predefined rules. In the case of combinatorial auctions, bids will also contain additional contingent characteristics. Furthermore, bids may or may not roll over into the next auction round under pre-specified rules or may be conditional upon specific conditions being met. Such factors can be defined in arbitrary ways by the auctioneer based upon what is deemed suitable for the specific application. Any set of predefined rules can be used for eligibility of the bid and bidder to participate in the relevant auction round, including, but not limited to, legal restrictions, credit limits on particular bidders, minimum/maximum bid amounts and sizes, etc. Cancellation of bids that do not meet such requirements comprises the validation stage of the process.

An auction round close occurs once a specific set of circumstances are met, as defined by the auctioneer. These could include: the availability of the resources, time elapsed since the preceding auction round close, receipt of sufficient number of bids, or any other conditions relevant to the specific application. Once an auction round closes, further computation occurs and bids would not be changeable or revocable. The time between when one auction round closes and the next one opens for bids can also be defined arbitrarily or by specific relevant conditions.

The valuation and bid ranking procedure operates after the auction round closes. The bid ranking procedure computes the bid value for each bid collected and eligible for participation according to any specific rules set. The most basic auction mechanisms equate the bid value with the bid itself. A lot of innovation went into providing more subtle bid valuation methods, reflecting additional features. In multi-attribute auctions, multiple attributes of the bid are combined into a single bid value [4]. One example of assigning bid value on a basis other than just a bid arises in Internet search pay-per-click advertising auctions in which a bid value is the product of the bid and click-through rate[9]. Other potential methods for assigning a value to a bid by the given bidder include additional information about the bid and the bidders, such as the time of the bid, geographical location of the bidders, etc. The final result of this procedure is the list of bidders ranked according to the values assigned to their bids. The present invention is applicable to any specific valuation and bid ranking procedure.

In the resource collection and ranking procedure, all resources available for allocation in the given round are ranked according to their intrinsic values, usually established by the auctioneer. A resource can be placed in an arbitrary order with respect to resources from which its intrinsic value cannot be differentiated. The resulting rankings may be collected in human accessible media (e.g., a printed list, list displayed on a screen etc.) or created in computer-assisted media to ensure timely and efficient processing of the information. Any relevant factors can be used to assign intrinsic value rank to the resources, as deemed appropriate to the specific application. Generally, the ranking reflects differences in intrinsic values of each individual unit of the resource. For example, value and therefore ranking of seats at the theater could be differentiated based on the distance from and the visibility of the stage. Likewise, the value and therefore ranking in Internet search pay-per-click advertisements is differentiated based on the position of the advertisement link on an Internet search query page [9].

The winner selection step takes each winner and establishes the mapping of bidders to resources. Traditional auction mechanisms map the bidder ranked k=1, 2, . . . up to the number of resources available, to the resource of the same rank.

The final step, pricing method computes the price to be paid by each bidder that receives a resource. The two main variants of pricing method step in the current state of the art are to pay the price equal to either own bid (FPSB) or the bid of the next highest bidder (SPSB). In the case where the bidders are ranked using other features in addition to the bid, the SPSB guarantees that the price paid by the bidder does not exceed the own bid of such bidder.

There may be additional contingencies which govern the exact amount of the final payment or whether there is to be any payment, such as whether the resource is fully utilized, delivered in accordance to preset terms, or other predefined rules. For instance, in commodities futures markets, different quality grades of the same resource have a fixed discount or premium to the basic price when they are delivered at expiry. Another example is Internet search pay-per-click advertisements, in which the final payment to the auctioneer is only triggered if a third party clicks on such advertisement.

Recurring auctions are increasingly popular form of markets for resources including but not limited to perishable goods (fresh flowers that wilt, fresh food that spoils and Internet search pay-per-click advertisements that appear only once immediately after a search query, etc.) and services for a specific time period (e.g., ticket for a designated flight, or for a specific concert, computer network bandwidth allocation for a predefined period of time or parking spot reservation for the specific time, as well as leases). Traditional auctions strive to motivate bidders to bid their true valuation of the goods traded. Yet, when successful in that respect, they also quickly divide the bidders into permanent winners (those with high true valuation of the traded resources) and permanent losers (those with low true valuation for the traded resources). In a recurring auction, the latter have no incentive to stay in future auction rounds, as they repeatedly lose the desired resource for which they are bidding. As a result, sooner or later, permanent losers of previous auction rounds drop out of the future rounds of a recurring auction. For purposes of the present invention, this phenomenon is referred to as a bidder drop. Bidder drop decreases the competitive pressure and therefore depresses the bids entered in future auction rounds [10].

SUMMARY OF THE INVENTION

The present invention relates to recurring auctions. It includes the system and method for conducting an auction repeatedly over time for a plurality of resources. The invention also includes a method for allocating traded resources to bidders in each auction round of a recurring auction in which the said allocation is based not only on the bid prices but also on bidder participation record in previous auction rounds. Any such method is referred to as a participant retention method.

The participant retention method preferably but not necessarily operates by selecting a certain number of bidders as belonging to the Definite Winner class in the current auction round, based strictly on their bid prices. At the same time, the remaining winners are selected from the remaining bidders taking into account a number of factors, including bidders' participation in the previous auction round or number of rounds, bids that they entered and the number and timings of resource allocations that they received in the previous auction round or a number of rounds. In one embodiment of the invention, this is accomplished by retaining some resources available in an auction round for the allocation to a set or subset of bidders from previous auction rounds. The specifics of methods for defining such resources and subsets of bidders are described below.

The selection of the winners enhancing participant retention can be accomplished using one of many possible participant retention methods. The winner selection method explicitly or implicitly classifies bidders into three classes, Definite Winner class (DW), Definite Loser class (DL) (both also present in traditional auction mechanism) and a new one called Possible Winner class (PW). There may be fewer resources assigned to the Possible Winner class than there are bidders in this class. In one embodiment of the invention, the participant retention method uses the number of consecutive losses together with the bid value as the criterion for selection of winners in Possible Winner class. In another embodiment, the bidders in Possible Winner class who lost the last round and did not decrease their bids are selected before the others to enhance participant retention. Yet another embodiment computes the difference between the already achieved and expected number of wins as a criterion for winner selection in Possible Winner class. When applied to the recurring auction, the invention results in higher and stable revenue of the auctioneer compared to the traditional auction mechanisms.

BRIEF DESCRIPTION OF THE DRAWINGS

The features of the invention believed to be novel are set forth in the appended claims. The invention, however, together with further objects and advantages thereof, may best be understood by reference to the following description taken in conjunction with the accompanying drawing(s) summarized below.

FIG. 1 illustrates the basic components and flow of information in auction.

FIG. 2 illustrates the novel winner selection method that is applied after the bids from the bidders are collected and the auction round is closed.

FIG. 3 illustrates the novel method of classifying of bidders in the present invention and compares it with the classification of bidders in the traditional auction mechanisms.

FIG. 4 illustrates relation of participant retention methodology to various repeated auction mechanisms.

FIG. 5 illustrates flowchart of the participation retention algorithm.

FIG. 6 illustrates the impact of resource waste and bidder drop problems on auction outcomes such as resources used and the average bidding price of the winners.

FIG. 7 illustrates how customers are classified into classes.

FIG. 8 illustrates the dependence of the average bidding price of winners on distribution of wealth of customers.

FIG. 9 illustrates loss of long-term fairness under different auction mechanisms.

DETAILED DESCRIPTION

An embodiment of the present invention relates to a computer storage product with a computer-readable medium having computer code thereon for performing various computer-implemented operations. The media and computer code may be those specially designed and constructed for the purposes of the present invention, or they may be of the kind well known and available to those having skill in the computer software arts. Examples of computer-readable media include, but are not limited to: magnetic media such as hard disks, floppy disks, and magnetic tape; optical media such as CD-ROMs and holographic devices; magneto-optical media such as floptical disks; flash memory; and hardware devices that are specially configured to store and execute program code, such as application-specific integrated circuits (“ASICs”), programmable logic devices (“PLDs”) and ROM and RAM devices. Examples of computer code include machine code, such as produced by a compiler, and files containing higher-level code that are executed by a computer using an interpreter. For example, an embodiment of the invention may be implemented using Java, C++, or any other programming language and development tools. Another embodiment of the invention may be implemented in hardwired circuitry in place of, or in combination with, machine-executable software instructions.

The foregoing description, for purposes of explanation, used specific nomenclature to provide a thorough understanding of the invention. However, it will be apparent to one skilled in the art that specific details are not required in order to practice the invention. Thus, the foregoing descriptions of specific embodiments of the invention are presented for purposes of illustration and description. They are not intended to be exhaustive or to limit the invention to the precise forms disclosed; obviously, many modifications and variations are possible in view of the above teachings. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications, they thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated. It is intended that the following claims and their equivalents define the scope of the invention.

The present invention provides a novel winner selection method in a recurring auction. As such, the invention fits seamlessly into the framework of an auction shown in FIG. 1. As described, the winner selection method is used when the collection of bids closes and after the bidders and resources are ranked. The box labeled winner selection in FIG. 1 is represented in the form of flowchart in FIG. 2 that illustrates the steps of winner selection in the present invention. These steps are further described below.

Step 1: Classification of Bidders

The first step of winner selection method is to perform classification of bidders into three classes: Definite Winner (DW), Definite Loser (DL) and Possible Winner (PW) class. Each bidder is classified into exactly one of the three classes. We will denote the number of bidders in each of those classes as N_(DW), N_(DL), N_(PW), respectively. Inside each class, bidders are ordered according to their ranks established in Step 3. Definite Winner class contains bidders with N_(DW) highest ranked bid values, while Definite Loser class contains bidders with N_(DL) lowest ranked bid values. In general, the present invention does not limit the sizes of the classes, except that the Possible Winner class is nonempty, so it could be that all the bidders are in the Possible Winner class (so, N_(PW)=N, N_(DW)=N_(DL)=0), or that no bidders are in the Definite Loser class (so, only N_(DL)=0), or that no bidder is assured of a win (so only N_(DW)=0), and many other combinations.

The described step happens after all bids for the current auction round have been collected and all bidders have been ranked in descending order of their bid values. Denoting the number of resources traded in this auction round by R, it should be noted that a traditional auction mechanism would award those resource to R highest ranked bidders, so in this case N_(DW)=R. Denoting the number of bidders in the current auction round by N, it should be observed that in the traditional auction mechanism the remaining N−R bidders will be definite losers in this auction round. Hence, a traditional auction mechanism has a Definite Loser class of size N_(DL)=N−R, and no Possible Winner class (N_(PW)=0). In contrast, in the present invention, the Possible Winner class can include any positive number of bidders, from one to all.

The Definite Winner class can be defined in one of two ways. Either (i) a fixed proportion of the highest ranking resources, r_(DW) is defined, so the top N_(DW)=r_(DW)*R (in other words, the size of Definite Winner class is determined by multiplying a fixed proportion of resources times the number of resources) ranking bidders comprise the DW class, or (ii) the Definite Winner reservation price, P_(DW), is defined and Definite Winner class consists of those bidder whose bid values are higher than P_(DW).

If a definite winner reservation price, denoted as P_(DW), is set, it should be selected at or above auctioneer's total expected revenue divided by the number of resources traded, so if all sales are made at this P_(DW), the auctioneer's revenue will meet his expectations.

Selecting the proper proportion of the resources designated for the Definite Winner class by choosing the fixed proportion of the resources factor r_(DW), requires careful analysis of bidding patterns, the desired number of bidders in each auction round, and willingness of bidders to continue participating in the future auction rounds despite the lack of winning of the desired resources. In the recurring auction, each bidder may have a drop point, also known as the bidder's tolerance to auction round losses, denoted as L, that is defined as the number of times that a bidder has not been allocated desired resources in consecutive auction rounds that will motivate the bidder to leave the recurring auction altogether. The maximum stable number of bidders in the Possible Winner class is R*(1−r_(DW))*(L−1) (which is equal to the number of resources not assigned to the Definite Winner class, and therefore assigned to the Possible Winner class, multiplied by one less than the bidder's drop point), and it is possible to achieve only under the most efficient participant retention method, because in such case each bidder in the Possible Winner class incurs exactly L−1 losses before a win. Hence, selection of factor r_(DW) not only impacts the size of the Definite Winner class but also limits the size of the Possible Winner class. The inventors' experiments indicate that for many bidder true valuation distributions, the optimal value of the fixed proportion of the resources factor r_(DW) is around ⅔ [10].

The Possible Winner class is defined either by (i) the reservation price P_(PW), so a bidder whose bid value is below this price belongs to Definite Loser class, or (ii) the maximum number of bidders in Possible Winner class is set, so the bidders whose rank is higher than N_(DW)+N_(PW) or whose bid value is 0 are in the Definite Loser class. In both cases Possible Winner class consist of the bidders allocated neither to Definite Winner nor Definite Loser class. With this notation, the number of resources assigned to the Possible Winner class is R−N_(DW) (which is the difference between the total number of resources and the number of resources allocated to Definite Winner class) and the effective participant retention requires that most of the time N_(PW)>R−N_(DW) (so the number of bidders in Possible Winner class is larger than the number of resources allocated to this class). Similarly, if both P_(DW) and P_(PW) are set, then the effective participant retention requires that P_(DW)>P_(PW) (so the Definite Winner reservation price is higher than the Possible Winner reservation price). The FIG. 3 shows the classification of bidders in the present invention.

The reservation price for Possible Winner class, P_(PW), if set, should be selected at or above the cost of each traded resource and the unit cost of conducting an auction round, so the auctioneer revenue from sales at this price will cover his costs.

By introducing two different reservation prices, the present invention addresses the problem of wasted resources that arises in auctions in which perishable goods or time-specific services are traded. Those are resources that lose value extremely rapidly even when unused. These goods cannot be effectively stored for future use without losing the majority of their value. Examples include fresh flowers, pay-per-click search advertisements that expire at the end of each search query, or fresh food, but also time-specific services such as ticket for a designated flight, or for a specific concert, or computer network bandwidth allocation for predefined period of time. In traditional auction methods, one reservation price is used. If fewer bidders exceed this price than there are resources available, then there would be unsold resources that would be wasted in case of perishable goods. The present invention introduces two reservation prices, and if fewer bidders exceed the reservation price for Definite Winner class, the resources will be offered to the bidders in Possible Winner class, avoiding the resource waste.

Selecting the proper size of the Possible Winner class requires careful analysis of bidding patterns, willingness of bidders to stay in the auction despite the losses, desired number of bidders in the auction and the quality of the participant retention method. As discussed above the stable number of bidders in the Possible Winner class cannot exceed (R−N_(DW))*(L−1) (which is equal to the number of resources allocated to the Possible Winner class times one less than the bidder's drop point), where L is the bidder drop point, also known as the bidder's tolerance to auction round losses. Thus, the total number of bidders that participate in the recurring auction permanently cannot exceed n=(R−N_(DW))*(L−1)+N_(DW) (which is just the sum of the size of the Definite Winner class and the upper limit of the size of the Possible Winner class). As discussed in [1], the optimal bid in a First Price Sealed Bid (FPSB) auction is the following fraction of the bidder's true valuation: (n−R)/(n−R+1) (which is the ratio of number of bidders who were not allocated a resource in an auction round to this number plus one). Consequently, larger n makes this fraction larger but requires smaller Definite Winner class (N_(DW)), so results in frequent allocation of resources to the lower bidding bidders. For many bidder true valuation distributions, the inventors observed that the optimal size of the Possible Winner class is around L*R/3, but the exact setting of this value should be found experimentally depending on the bidder true valuation distribution, bidder drop point, the number of goods traded and other factors.

Step 2: Winner Selection in Possible Winner class

After the bidder's classification is done according to step 1, the winner selection process is as follows.

The bidders in Definite Winner class are allocated the top min(R, N_(DW)) (the number of resources in Definite Winner class, or all resources if this number is larger than the total number of resources) resources in the order of their ranking. Of course, all resources R are allocated to Possible Winner class if Definite Winner class is empty (N_(DW)=0).

The bidders in Definite Loser class are denied any resources in the current auction round with no further considerations.

The winner selection in the Possible Winner class is determined by the participant retention methodology that takes into account such factors as bidder's participation in the current and previous auction rounds, bids that he entered, his number of wins, his number of consecutive losses, etc. All of these factors are used to compute the retention score that combined with the bidder's bid value is used to re-rank the bidders in the Possible Winner class. After the re-ranking, the R−N_(DW) highest ranking bidders in the Possible Winner class are assigned the remaining ranked resources in the order of their final rank.

Two distinct methods were developed in the present invention to enhance participant retention in recurring auctions. The first approach is to select bidders in a way aiming at decreasing their probability of dropping out of the next auction round. The second approach is to encourage bidders to participate in future auction rounds by providing appropriate reward for their participation. The U.S. Provisional Patent Application No. 60/622,028, filed Oct. 26, 2004, the entire disclosure of which is incorporated herein by reference, contains a detailed description of the preferred embodiment of the invention. Pertinent portions of this provisional application have been explicitly incorporated and are set forth below and in the drawings.

There are two major innovations included in this invention. One is the idea of the nontraditional auction, in which each winner is selected with a certain probability, dependent upon the bidding price and behavior and outcome of the previous auction rounds, from a subset of bidders. The traditional auction mechanisms separate bidders into two classes: (i) traditional winners who are assigned auctioned goods or services, and (ii) traditional losers who are not assigned any goods or services. In other words, the probability of win in the traditional auction is either 1 or 0 for each winner and is strictly defined by the rank ordering of bid prices. In the present invention, for an additional class of users, called potential winners, the probability of win is p, 0<p<1. While these are also defined by the rank order of bid price, the non-binary state creates an incentive for a greater subset of potential participants to maintain participation in the long term.

Another major new idea in the present invention is the participant retention methodology in the recurrent auction for various types of resources. As shown in FIG. 4, the participant retention methodology mechanism is meta-mechanism that can be applied to the various auction mechanisms as long as the auction itself is recurring with the overlapping customers, or more precisely, with the customers drawn from the stable group. The general participant retention methodology mechanism is sketched in FIG. 5.

The differentiation between three classes of definite winners, DW, potential winners, PW and definite losers, DL, is a key to establishing the winning probability and frequency of wins in the auction. For DW bidders set, the probability of win is 100%. For PW bidders set, the probability of win is anywhere between 0% and 100% based on various attributes (such as the number of consecutive losses, bidding price) and history of bidding or even luck (in pure randomized winner selection algorithm). For DL bidders set, the probability of win is 0%.

The participant retention methodology algorithm is applied to the bidders from the PW set in each auction round. It should depend on the type of market as described in terms of participations, property of resources, etc., and the wealth (that is income) distribution of the bidders. For example, for a homogeneous premium quality of network service, VLLF (Valuable Last Loser First) algorithm can be used, as described below.

Currently, we identified the following variations of the participant retention methodology algorithm.

LMA (Last Minute Allocation), in which the auctioneer predict the each bidder's drop point (i.e., the Maximum Tolerance to Consecutive Loss, L), and then allocates the resource to the bidders whose consecutive loss is equal to (L−1). There are various ways of predicting the bidder's drop point, L.

RAP (Random Allocation with Probability dependent on rank), in which the winners are selected randomly, each with probability 1/L+(R−Rdw−Rpw/L)*bi/b, where bi is the bid of the bidder in PW set and b is the sum of all bids made by bidders in set PW for a round in which Rpw<L*(R−Rd).

The precise modeling of a customer behavior is a critical part of the validity of models used in the designing of auction based dynamic pricing schemes. However, the previously considered auctions for network services disregarded the recurring nature of those auctions and their impact upon participant incentives. Generally, an allocation of network services is made for a specific time only, and once these resources become free, the network service provider needs to organize another auction to offer them to the customers again. Hence, an auction for network services should be regarded as a recurring one. For such auction, using traditional mechanisms, such as English or Vickrey auctions, may result in an inevitable starvation of certain customers. As a result of such starvation, the affected customers may decide to drop out of the future auction rounds, thereby decreasing the long-term demand for the traded goods unless new participants arise. In such a development, the network service provider cannot maintain a revenue stream above a minimal threshold. The conclusion is that in a recurring auction to stabilize revenue, the network service provider must prevent the price collapse and that means the control of the supply of resources as well as the resolution to the customer drop problem. Although a lot of attention was directed to the control of the resource supply, to the best of our knowledge, the control of the customer drop problem has not been addressed.

Here, we describe application of a novel pricing mechanism for a recurring auction to short-term contracts for network service. This mechanism focuses on reducing the customer drop problem, eliminating the waste of resources and correcting the asymmetry of the negotiation power balance from which the traditional auction mechanisms suffer. The proposed mechanism is applicable to a multiple winners, discriminatory pricing, and sealed bid auction with the seller reservation price.

From the market structure point of view, an auction for network services can be regarded as an operated market that has one-to-many participants (i.e., one network service provider and many customers), and in which multiple units of homogeneous goods are traded. The traded goods are network resources for premium quality, homogeneous network service that is requested recurrently by the customers for a specific time interval. Successful customers make contracts with a network service provider at the price that they bid in an auction for the desired network service at the desired time interval. We assume that the traded services are inelastic network applications, such as real-time voice and video applications that require the fixed amount of network resources to achieve the adequate quality of service (QoS). For this reason, the predetermined part of network resources is allocated to the traded services. The size of this part, assumed here to be constant for all auction rounds, defines the upper limit on the number of winners in each auction round.

Our negotiation scenario is based on two types of contracts. One type, long-term contracts, is used for network services with the best-effort quality. Another type, short-term contracts that are awarded via an auction, applies to the guaranteed premium quality network service. Our negotiation scenario focuses on recurring, short-term contracts only.

The quality of network services is decided by the capacity of network resources (such as bandwidth, etc.) that are allocated to them. Since network resources assigned for a given time interval are perishable (that is they perish if not used), we can characterize them as time sensitive goods.

With recurring demand for and time sensitivity to network resources, the traditional auction mechanisms, when applied to an auction for network services, cause the following problems.

Asymmetric Balance of Negotiation Power:

In most of the general auction mechanisms, the prices bid in an auction are dependent on the customer's willingness to pay for the traded goods. This means that intentions of only customers, but not of the network service provider, are reflected in the auction winning prices.

Resource Waste:

To resolve the asymmetric balance of negotiation power problem, the seller's reservation price has been introduced into the general auction mechanism. Only bids higher than the seller's reservation price are considered during winner selection. However, in case of time sensitive goods, such as network services, the seller's reservation price causes resource waste. Resources unused because of the restriction on the number of winners imposed by the reservation price are wasted.

Bidder Drop Problem:

Prices bid in an auction are dependent on the willingness of each customer to pay. This willingness in turn is expressed as the customer true valuation. Each customer wealth influences the upper bound on the customer's willingness to pay. An uneven wealth distribution can cause starvation of poor customers in a recurring auction. Most previous auction studies regarded the starvation as one of the methods for decreasing customer demand. A frequent starvation for the traded goods, however, also decreases the customer's interest in future auction rounds. In such situation, if customers conclude that it is impossible or unlikely that they will win at the price that they are willing to pay, they will not participate in future auction rounds. In our negotiation scenarios of a recurring auction, each customer's drop out of an auction round decreases the number of active customers. We will refer to the active customers as bidders. Such a drop in the number of bidders gradually decreases the level of price competition. In the long run, when the number of bidders drops below a certain level, the seller can not guarantee the expected revenues in the future auction rounds. This is because the remaining bidders constantly win and as a result they may decrease their bidding prices for future auction rounds in order to maximize their expected profit. Thus, in such a scenario, the bidding price guaranteeing a win in an auction round may collapse to a very low level.

In addition to the unbalanced wealth distribution, the potential substitution of premium quality network service with best-effort service is another important reason for motivating customers to drop out of the auction. According to our assumptions, customers who participate in an auction for premium quality network service already have entered a long-term contract for the best-effort quality network services. Thus, even if they lose in an auction, they always have an alternative (i.e., the best-effort quality network service) available for their requests.

The importance of bidder drop control (i.e., maintaining a sufficiently high number of active customers) in an auction can be shown by the following theoretical reasoning that is used to justify the first price sealed bid auction.

Under the assumptions of a uniform distribution of bidder's private true valuations, and risk neutral bidders, the optimal bidding price (i.e., that is the price that optimizes the bidder expected profit) for bidder i in each auction round is

${b_{i}^{*} = {\left( \frac{n - k}{n - k + 1} \right) \cdot t_{i}}},$

where b_(i)* denotes the optimal bidding price of bidder i, t_(i) represents the private true valuation of bidder i, n denotes the number of active bidders (i.e., participants in an auction), and k represents the number of possible winners in each auction round based on available resources.

To maximize the seller's income from an auction, the optimal bidding price of each bidder should be close to his true valuation. To avoid wasting of resources, the number of winners in each auction round should be constant. Hence, to keep the optimal bidding price from above equation close to the true valuation, the number of bidders should be high because of coefficient (n−k)/(n−k+1) of the optimal bidding price.

Our experimental results show that the three described above motivating problems indeed arise in our negotiation scenarios. As shown in FIG. 6(A), 28.6% of network resources are wasted by allocating resources only to the qualified customers in each auction with the reservation price. FIG. 6(B) shows that the bidder drop rate in a recurring auction directly affects the average winning price (i.e., the revenue of the seller) in each auction round.

To solve the motivating problems in the auction based dynamic pricing scheme for network services, we propose a novel auction mechanism based on novel winners policy as described in the next section. This mechanism (i) maximizes the network service provider's revenue, (ii) minimizes the loss of fairness that is caused by the bidders dropping out of an auction, and (iii) achieves social justice in terms of the network resource distribution in a recurring auction.

The main idea of the winner selection in a recurring auction with the new winner policy is based on the demand-supply principle of microeconomics. When the overall bid price decreases during a recurring auction, the minimum market clearing price decreases. To maintain or increase the minimum market-clearing price, the service provider should decrease the supply of resources from. Reversely, when the overall bid price increases, the service provider may increase the supply. In our negotiation scenario, however, when the service provider decreases the supply of network resources for the given time period, the unsold resources are wasted. Thus, in the proposed auction mechanism, the “unsold” network resources are assigned to the bidders who have high probability of dropping out in the forthcoming auction round. This assignment prevents such drop. Hence, the proposed auction mechanism can achieve the service provider's desired revenue by keeping enough bidders in the auction to maintain the competition for resources. Simultaneously, using “unsold” resources for bidder drop control can resolve the resource waste problem and maximize the number of winners.

We consider an auction in which there are n+1 bidders, denoted by i=0, . . . , n, including n customers, i=1 . . . n, who already made a long-term contract with a network service provider i=0. Each bidder enters her bidding price b₀, b₁, b₂, . . . , b_(n) in an auction round. We assume a sealed bidding, thus only a bidder and network service provider can communicate.

There are also R units of network resources that are assigned to the premium quality homogeneous network service for the predefined time period. The network service provider trades these assignments in auction round. Each customer requires one unit of network resources for the premium quality network service.

The first step of an auction with new winners policy is to define the class of each customer based on customer's bidding price b_(i), where i=1, . . . , n, and network service provider's bidding price b₀ in each auction round. After n customers bid in an auction round, network service provider classifies each customer into the Definite Winner (DW) and Definite Loser (DL) classes based on the ascending rank of each customer's bidding price and available resources. Let r_(i), denote the rank of bidder i. The DW and DL classes represent the customers who would be winners and losers, respectively, in a traditional auction. The numbers of customers in the DW class, denoted by N_(DW), and the DL class, denoted by N_(DL), are N_(DW)=R and N_(DL)=n−N_(DW)=n−R.

After bidding the reservation price b₀, the network service provider classifies n customers into Definite Winner (DW), Definite Loser (DL), and Possible Winner (PW) classes using the following conditions:

iεDW if b _(i) ≧b ₀ & r_(i) >n−N _(DW) , i=1,2, . . . ,n

iεDL if b _(i)=0, i=1,2, . . . ,n.

iεPW otherwise.

The DW class customers can be winner without any additional considerations, since they bid higher price than network service provider did. The DL class represents the customers who already dropped out of the auction because they consecutively lost more times than their tolerance allows. The customers who are in the PW class can be winners or losers depending on the bidder drop control mechanism. The Winner Portion of Possible Winner class (WPPW) is defined by the capacity of the network resources that are reserved for the bidder drop control mechanism. Thus, the number of customers N_(WPPW) who can be winners in the PW class is N_(WPPW)=R−N_(DW), as shown in FIG. 7.

Valuable Last Loser First (VLLF) Algorithm:

By definition, the bidder drop control mechanism applies only to customers of the PW class, so it must include the efficient strategy for selecting winners in this class. For this purpose, we propose the Valuable Last Loser First (VLLF) algorithm that consists of two phases. In the first phase, the VLLF algorithm selects customers in the PW class who have high probability of dropping out of the forthcoming auction round. The second phase of the VLLF algorithm compensates for the loss of fairness resulting from the first phase.

In the first phase of the VLLF algorithm, the bidders who lost in the current auction round but bid higher price than in the previous auction round are marked as potential winners. The marked bidders are ranked according to their bidding price and up to N_(WPPW) highest ranked marked bidders are selected as the winners of the current auction round. If the number of the marked bidders is less than N_(WPPW), the remaining resources are allocated in the second phase of the algorithm. The winner selection in the first phase is influenced by the bids in the previous auction round, so there could be some loss of fairness. To compensate for it, in the second phase, the highest bidding unmarked bidders in the WL class are selected as winners of the remaining resources. By marking only those last losers who bid higher in the current round than in the previous one, the algorithm prevents bidders with low bidding patterns from becoming winners.

The bidding price of the network service provider defines the minimum bid needed for customers to belong to the DW class (so it plays the same role as the reservation price does in traditional auction). Accordingly, this price is also called the DW class Minimum Price (DWMP). Finding the optimal DWMP is equivalent to finding the optimal amount of network resources to be reserved for the bidder drop control.

We define C as the minimum cost of a unit of traded resources. The network service provider should set this cost after considering internal and external expenses according to well established industrial practice. This cost can also be interpreted as the network service provider's desired minimum price for the unit of network resources.

DWMP (i.e., the bidding price of the network service provider) needs to be selected properly to make the VLLF bidder drop control algorithm efficient.

The minimum revenue of an auction round with the VLLF bidder drop control algorithm should be larger than, or equal to, the network service provider's desired revenue:

b₀·N_(DW)+P_(WPPW)·(R−N_(DW))≧C_(m)·R, where P_(WPPW) represents the minimum bidding price of winners from the WL class. To guarantee the network service provider's desired revenue, P_(WPPW) should be

$P_{WPPW} \geq {\frac{{C_{m} \cdot R} - {b_{0} \cdot N_{DW}}}{R - N_{DW}}.}$

To control bidder drops efficiently, N_(DW) should be less than R because there should be some units of network resources available for the VLLF bidder drop control. Hence, the minimum revenue of an auction round is constrained by the following conditions on N_(DW), and P_(WPPW): 0<N_(DW)<R and 0<P_(WPPW)<b₀, limiting the range of the optimal DWMP values to C_(m)<b₀<C_(m)R/R_(DW). Therefore, the network service provider should bid a higher price than her desired minimum cost of a unit of network resources to maintain the desired revenue of each auction round.

In defining the upper bound of a range for optimal DWMP values, the network service provider should consider the interrelationship between the three types of customer's classes, the revenue and the fairness. If the network service provider increases the DWMP, the number of customers in the DW class decreases (i.e., N_(DW) decreases). This change results in increasing the number of units of the network resources reserved for the bidder drop control. Thus, in this case, the number of customers in the DL class decreases and the total revenue usually, but not necessarily increases. Increasing the number of units of the network resources reserved for the bidder drop control, however, decreases the fairness of the network resource allocation. This is because the winners in the first phase of the VLLF algorithm are selected based not only on their current bidding prices but also on their bidding prices and status in the previous auction round.

The reverse case (i.e., decreasing DWMP) usually but not necessarily decreases the revenue of the network service provider and increases the fairness by decreasing the number of units available for the bidder drop control. Accordingly, in deciding the upper bound of DWMP, the network service provider should consider maximizing revenues and minimizing the loss of fairness under the trade-off relationship between the revenue and fairness. Based on many experiments conducted under the various customer wealth distributions, we propose 2:3 rule (every two out of three, or 66.67% of the network resources allocated to the DW class) for the near optimal distribution of the network resources between the DW class and the pool of network resources reserved for the VLLF bidder drop control. By using the 2:3 rule, we can redefine the upper bound of the range for the optimal value of the network service provider's bidding price as 0<b₀−C_(m)<C_(m)/2.

Our experimental results show that, in most cases, the mean of the bidding prices of the bidders in the PW class in each auction round is close to the their true valuations of traded goods. Based on these experimental results, we propose a simple and adaptive way for deciding the network service provider's bidding price. In each auction round, after the network service provider ranks customer's bidding prices in ascending order, the mean of the bidding prices P_(aPW) of bidders in the PW class is defined as

${P_{aPW} = \frac{\sum\limits_{i = {n - N_{PW} + 1}}^{n}\; b_{r_{i}}}{N_{PW}}},$

where r_(k) represents the k^(th) ranked bidder within the ascending order of the bidding prices. In the PW class average approach, the network service provider selects P_(aPW) as her bidding price b₀ in that auction round, if its value is within the range defined by above equation. Otherwise, C_(m) is selected as the network service provider's bidding price b₀.

In our experiments, we compare the following three auction mechanisms for the single item, multiple winners, discriminatory pricing, and sealed bid recurring auction for the short-term contracts on homogeneous network services:

Traditional Auction (TA) denotes an auction mechanism that has no bidder drop control mechanism. In TA, bidders drop during the recurring auction as a result of starvation.

Traditional Auction with No Bidder Drop Assumption (TANBDA) represents a traditional auction mechanism in which bidders never drop during the recurring auction in spite of starvation (i.e., despite the consecutive losses in the recurring auction).

Auction with the New Winners Policy represents an auction mechanism that supports the VLLF bidder drop control algorithm with the PW class average bidding approach described in the previous section.

The wealth of each customer is the main factor that limits her willingness to pay (i.e., each customer's true valuation) in the auction. For this reason, we can interpret the wealth distribution as a distribution of the upper bound on willingness to pay. We set the network service provider's minimum cost of a unit of the network resources at 5. Based on the network service provider's minimum cost, we consider three types of the standard distributions of the upper bound on willingness to pay among the customers: Exponential distribution with mean 5, Uniform distribution over [1, 10] range, and Gaussian distribution with a mean of 5.

There are 100 customers (i.e. bidders) in our experiments. We assume that the initial bidding price is randomly selected from the range [t_(i)/2, t_(i)], where t_(i) represents the upper bound on customer i willingness to pay. The sealed bidding assumption makes each bidder's bidding behavior independent of others. However, in a recurring auction, the bidding behavior is influenced by results of the previous auction rounds, because only the win/loss outcome is informed to the bidders. Based on the assumption of risk neutral bidders, the bidders will maximize the expected profit. All these considerations motivated us to assume the following bidding behavior in a recurring auction.

If a bidder lost in the last auction round, he increases his bidding price by the amount of α·b_(i) ¹ to increase his win probability in the current auction round, where α denotes the increase coefficient and 0≦α≦1. b_(i) ¹ represents the bidding price of bidder i in the last auction round. This increase of bidding price is limited by the upper bound on willingness to pay. If a bidder won in the last auction round, she, with equal probability of 0.5, either decreases the bidding price by a factor β or maintains it unchanged. The decrease attempts to maximize the expected profit. α and β are set in the experiments to 0.2. The minimum bidding price of a bidder is 0.1. If a customer drops out of an auction, his bidding price is set to 0. There are 50 units of resources available for allocation in each auction round.

The customer's tolerance of consecutive losses, abbreviated as L, denotes the maximum number of consecutive losses that a customer can tolerate before dropping out of an auction. L of each customer is uniformly distributed over the range of [2,10]. Based on the above experimental scenarios, we assume that initially each bidder wants to participate in an auction round and the auction is executed 2000 times.

Our experiments focus on the network service provider's revenue and the fairness of the network resource allocation during the recurring auction. The fairness in auction means that a bidder with a bid higher than any of the winners should be a winner as well. In our experiments, the network service provider's revenue is proportional to the average bidding price of a winner in each auction round, so we use the latter as a measure of the former. We also measure the number of wins for each customer in 2000 rounds of the recurring auction. The resulting distribution is a metric of fairness, because higher bidding customers should be more frequent winners than the lower bidding ones. Fairness of TANBDA is optimal, because a bidder with the bid higher than any of the winner is always a winner. Additionally, by the no bidder drop assumption, TANBDA never loses a customer with the high willingness to pay but the low L. This means that TANBDA can prevent the loss of fairness that results from the low L. Thus, we can measure the loss of fairness of TA and the new auction mechanism mechanisms by their degree of the deviation from the fairness of TANBDA. We measure the auction fairness LF_(k) for auction mechanism k by the distribution of wins between the customers:

${{LF}_{k} = {\frac{\sum\limits_{i = 1}^{n}\; {{{{NW}_{TANBDA}(i)} - {{NW}_{k}(i)}}}}{N_{Auction} \cdot N_{Total\_ Auction}} \cdot 100}},$

where n denotes the total number of customers in the recurring auction, NW_(TANBDA)(i) and NW_(k)(i) represent the total number of wins by bidder i during N_(Total) _(—) _(Auction) of auction rounds in TANBDA and auction mechanism k, respectively. N_(Auction) denotes the total number of winners in each auction round. The experimental results of TANBDA are impossible to achieve in the real recurring auction, because the no bidder drop assumption is unrealistic. In the real world, starvation will be triggered by the uneven wealth distribution combined with the customer's ability to substitute the premium quality network services with the best-effort ones. Thus, in our experimentation, TANBDA is only used for comparison.

TA cannot guarantee maintaining the network service provider's desired revenue in an auction, because the inevitable bidder drops will decrease the price competition between customers who continue participation. Accordingly, the remaining customers will decrease their bidding price in the forthcoming auction rounds to maximize their expected profit. This behavior is based on the risk neutral bidder assumption since the winning probability is increased in an auction with fewer competitors. In the long run, the revenue of each auction round will plunge to a very low level (i.e., below 1.0), compared to the network service provider minimum cost (here 5.0). An efficient bidder drop control, however, can maintain the number of price competitors permanently high in each auction round. Thus, the network service provider can preserve the near optimal level of the desired revenue in each auction round. As shown in FIG. 8, the described above phenomenon appears under various wealth distributions in the recurring auction for short-term contracts on network services.

Remarkably, as shown in FIG. 9, the loss of fairness of the new auction mechanism is lower than that of TA under the various wealth distributions. This means that the fairness of the new auction mechanism is higher than the fairness of TA when bidders are allowed to drop out of an auction. This phenomenon results from the fact that TA cannot prevent the loss of fairness that is caused by the higher bidders dropping out of an auction as a result of exceeding their L (i.e., TA cannot prevent a customer who is willing to pay high prices but has the low L from dropping out of an auction). Even though TA maintains higher fairness than the new auction mechanism in each auction round, because customers in the PW class become winners in TA, remarkably, the new auction mechanism suffers lower loss of fairness during the recurring auction. This is because the loss of fairness that results from L is the dominating factor in the recurring auction.

We also simulated the more general case of an auction in which a bidder who dropped out can return when the winning price becomes sufficiently low. For this case, the experimental results show that the revenue of the network service provider settles somewhere between the revenues of TA and TANBDA. This is not surprising because TA and TANBDA are border cases of the general one. The revenue of TA case sets the lower bound of the revenue of the general case because there are no bidders returning during the recurring auction. The revenue of TANBDA sets the upper bound because all bidders return to the recurring auction even n that case.

Therefore, the new auction mechanism can achieve the increased revenue and decreased loss of fairness in a recurring auction compared to the traditional auction mechanisms.

Additionally, the winning distribution of the new auction mechanism auction shows that the proposed pricing mechanism can achieve higher social justice than TA. Even poor customers have a non-zero probability of winning in the new auction mechanism auction thanks to the VLLF bidder drop control algorithm. For this reason, the wins are widely distributed regardless of a distribution of the customer wealth. This property of our mechanism is important when the network resources are viewed as a public resource. In short, the proposed the new auction mechanism auction can stabilize the network service provider's revenue, minimize the loss of fairness, and achieve better social justice under the trade-off relationship between these three goals.

The following additional methods were specifically developed as the preferred embodiment of the participant retention methodology.

Many other bidder retention methods being a part of the present invention can be applied to accommodate specific goals of the auctioneer while relying on re-ranking of bidders in the Possible Winner class to increase bidder participation in future auction rounds. Some of them, but not all, are described below.

Last Minute Allocation (LMA):

In a recurring auction, each bidder may have a drop point, also known as the bidder's tolerance to auction round losses, denoted as L, that is defined as the number of consecutive losses in the subsequent auction rounds that will motivate the bidder to leave the recurring auction altogether. In LMA method, the auctioneer predicts each bidder's drop point L and then all bidders in Possible Winner class whose number of consecutive losses is equal to L−1 and whose bid is no smaller than the bid in the previous auction round, have their bid value increased by B. There are various ways of predicting the bidder's drop point that could be used in implementing this method. One, for example could be to keep the average or minimum number of consecutive losses for the bidders who actually dropped out of the recurring auction to predict the drop point for the remaining bidders.

Random Allocation (RA):

a bidder ranked k in Possible Winner class is selected as a winners randomly, with probability p_(k), that, for example could be equal (R−N_(DW))/N_(PW) regardless of the bidder rank. However, there is no restriction on probability p_(k) except that all those probabilities add up to the number or resources available for Possible Winner class (that is to R−N_(DW)).

Loss Increment Allocation (LIA):

This method assigns to each bidder with rank k in Possible Winner class, either multiplicative or additive bid increment I_(k) and then the bid value is modified accordingly (for multiplicative bid increment the bid value v becomes v*I_(k) and for the additive bid increment the new bid value is v+I_(k)). There are no limitations on how increment I_(k) is determined. One embodiment of this method defines the multiplicative bid increment as I_(k)=1+0.01*m, where m denotes the number of consecutive losses that the bidder sustained in the previous auction rounds.

The preferred embodiment of the second approach of participant retention methodology is the following method and software program.

Participation Incentive (PI):

Under this method, each bidder is rewarded for participation in the current and previous auction rounds with the score WS, defined for each bidder ranked i in Possible Winner class as the difference between the product of k-th power of bid value of bidder ranked i and the number of auction round that he participated in divided by coefficient a and the number of winning rounds, that can be expressed algebraically as follows:

WS _(i) =b _(i) ^(k) NP _(i) /α−NW _(i),  (1)

where NP_(i) and NW_(i) denote the cumulative number of times that bidder ranked i participated and won, respectively, up to and including the current auction round. Since the outcome of the current auction round is yet unknown, NP_(i)>NW_(i). The term b_(i) ^(k) NP_(i)/a represents the expected number of wins until the current auction round; a is a coefficient that controls the expected number of wins and k is a coefficient that controls how the differences between bid values affects the probability of win. Thus, the winning score WS, of bidder ranked i in Possible Winner class represents the difference between the expected and experienced numbers of wins. The Participation Incentive method assumes that higher the winning score of a bidder is, higher the probability of him dropping out of the future auction rounds is because more below his expectations the winnings are. For this reason, the Participation Incentive method re-ranks the bidders in the Possible Winner class in the decreasing order of their winning scores and up to R−N_(DW) highest re-ranked bidders in this class are selected as winners of the current auction round.

As shown by equation (1), the participation of a loser of the last auction round is rewarded directly by increasing her winning score in the current and future auction rounds. Therefore, the PI participant retention method can control bidder drop problem by encouraging bidders' participation in future auction rounds.

If in equation (1), coefficient a is increased, the effect of the bid value in the winning score is diminished. Thus, the lower bidding bidders experience more wins and the range of winners over the original ranking is broadened over Possible Winner class. Reversely, if coefficient a is decreased, the win distribution narrows and concentrates on the higher bidding bidders in Possible Winner class. The optimal value of coefficient a dependents on the auctioneer's marketing strategy. In the preferred embodiment of this invention, coefficient a is set to the value that makes the average value of winning score of all bidders equal to zero. Since in each round, all bidders in Possible Winner class increase their winning scores cumulatively by

$\sum\limits_{i = 1}^{N_{PW}}\; \frac{b_{i}^{k}}{a}$

(which is the sum of k-th powers of their bids divided by the coefficient a) and at the same time their winning scores decrease cumulatively by R−N_(DW) wins (the number of resources allocated to Possible Winner class), the balancing value of coefficient a is equal to the sum of k-th powers of all bid values of bidders in Possible Winner class divided by the number of resources allocated to this class (that is R−N_(DW)).

Pricing Methods:

Once the winners are selected, the prices for the resources allocated to the winners are established. In this process, the prices are determined by the original bids of each winner, regardless of the changes made to the bids during winner selection. However, the bidders who are the winners thanks to increasing their bid values through participant retention method win the resources above their original rank, prices charged to them can be computed as the minimum of their bid and the price to be paid by the bidder with the original rank that the winner acquired through participant retention method. In case of the First Price Sealed Bid (FPSB) auction, this would not change the pricing, as the winners would simply pay according to their bids. However, in case of the Second Price Sealed Bid (SPSB) auction, the prices to be paid could change.

In general, the present invention is applicable to an auction system and design, regardless of pricing method employed. In one embodiment of the present invention, a uniform pricing method is used in which the bidders in Definite Winner class are charged their reservation price P_(DW) and the winners in Possible Winner class are charged their reservation price P_(PW). In another embodiment of the present invention, a discriminatory pricing method is employed in which each winner is charged the price that is either a fraction of his bid defined by a coefficient f (so the price for a bidder with bid b is f*b), or equal to the bid of the bidder with the rank next to the winner, or a combination of those two prices. The coefficient f could be any positive number less or equal to 1 and it could be the same or different for each bidder. Yet another embodiment of the present invention uses discriminatory pricing for one class and uniform pricing for another class. For example, uniform price P_(DW) is charged to all bidders in Definite Winner class while each winner in Possible Winner class is charged the price that is a fraction of his bid.

The following references may be related to the present invention:

-   [1] R. McAfee and P. J. McMillan (1997), “Auction and Bidding”,     Journal of Economic Literature, 25:699-738. -   [2] V. Krishna, Auction Theory (2002), Academic Press, San Diego. -   [3] W. Vickrey (1961), “Counter speculation, Auction, and     Competitive Sealed Tenders”, Journal of Finance, 16(1). -   [4] M. Bichler, M. Kaukal, and A. Segev (1999), “Multi-attribute     auctions for electronic procurement”, Proc. 1^(st) IBM IAC Workshop     on Internet based Negotiation Technologies, Yorktown Heights, N.Y. -   [5] T. Sandholm (2000), “Approaches to winner determination in     combinatorial auctions”, Decision Support System, 28 (1):165-176. -   [6] M. H. Rothkopf, and A. Pekec (1998), “Computationally Manageable     Combinatorial Auction”, Proc. Maryland Auction Conference, Maryland. -   [7] T. Sandholm (1999), “Automated Negotiation”, Communication of     the ACM, 42(3): 84-85. -   [8] H. Varian (1995), “Economic Mechanism Design for Computerized     Agents”, Proc. Usenix Workshop on Electronic Commerce, New York. -   [9] N. Brooks (2004), “The Atlas Rank Report: How Search Engine     Impacts Traffic”, Atlas Institute. -   [10] J. S. Lee and B. K. Szymanski (2004), “A Novel Auction     Mechanism for Selling Time-Sensitive E-Service”, Proc. 7th     International IEEE Conference on E-Commerce Technology (CEC'05),     Munich, Germany.

The knowledge possessed by someone of ordinary skill in the art at the time of this disclosure, including but not limited to the prior art disclosed with this application, is understood to be part and parcel of this disclosure and is implicitly incorporated by reference herein, even if in the interest of economy express statements about the specific knowledge understood to be possessed by someone of ordinary skill are omitted from this disclosure. While reference may be made in this disclosure to the invention comprising a combination of a plurality of elements, it is also understood that this invention is regarded to comprise combinations which omit or exclude one or more of such elements, even if this omission or exclusion of an element or elements is not expressly stated herein, unless it is expressly stated herein that an element is essential to applicant's combination and cannot be omitted. It is further understood that the related prior art may include elements from which this invention may be distinguished by negative claim limitations, even without any express statement of such negative limitations herein. It is to be understood, between the positive statements of applicant's invention expressly stated herein, and the prior art and knowledge of the prior art by those of ordinary skill which is incorporated herein even if not expressly reproduced here for reasons of economy, that any and all such negative claim limitations supported by the prior art are also considered to be within the scope of this disclosure and its associated claims, even absent any express statement herein about any particular negative claim limitations.

Finally, while only certain preferred features of the invention have been illustrated and described, many modifications, changes and substitutions will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention. 

I claim:
 1. A method for an auctioneer to allocate perishable or time-specific resources to bids in a plurality of auction rounds, wherein allocating resources to bids in each auction round is executed on at least one computer comprising computer-readable medium with computer executable instructions to perform various computer-implemented operations necessary for timely execution of said allocation, comprising: (a) said computer receiving in its storage and thus having available a list of perishable goods or time-specific resources traded in a given auction round, wherein said list of resources to be traded in said given round is ranked according to factors set by the auctioneer and each resource is traded only in said auction round because said resource loses value if not allocated because it is perishable or time-specific; (b) said computer receiving bids relevant to said auction round wherein each bid comprises a bid price for allocation of one of the resources listed in said list of resources received in step (a), and information identifying a participant bidder making said bid; (c) for each of said bid prices received in step (b), said computer: (c1) establishing probabilities of winning the resource in a single auction round wherein a difference between the probabilities computed for two bids is a non-decreasing function of difference between bid prices of the two bids whereby bidders of these two bids are motivated to raise their bid prices to increase their probability of resource allocation, (c2) sorting said probabilities of winning in order of said probabilities of winning, (c3) not restricting participation in a future auction round based on a participant bidder winning or losing in said given round or in a previous round; and (d) said computer allocating said resources to said bids based on said probabilities of winning established in said step (c), rather than based on said bid prices received in said step (b) by selecting sequentially, in the order the said sorted probabilities in (d), bidders as winners randomly based on their probabilities established in (c), until either all resources are allocated, or the number of unprocessed bidders becomes equal to the number of unallocated resources remaining, in which case the remaining bidders are allocated the remaining resources in the order of their said sorted probabilities.
 2. The method of claim 1 wherein an auctioneer sets a minimum bid price and step (c1) is executed only for bids with bid prices not lower than said minimum bid price.
 3. The method of claim 1 wherein an auctioneer sets a maximum number of bids for which step (c1) is executed.
 4. The method of claim 1 wherein the probabilities assigned to each bid in step (c1) are the non-increasing function of the bid rank.
 5. The method of claim 1 wherein the same probability is assigned to each bid in step (c1).
 6. The method of claim 1 wherein the probability of 1 is assigned to each bid in step (c1).
 7. The method of claim 1 wherein resources traded in each auction round comprise spaces for paid advertisements on at least one internet page.
 8. A method for an auctioneer to allocate perishable or time-specific resources to bids in a plurality of auction rounds, wherein allocating resources to bids in each auction round is executed on at least one computer comprising computer-readable medium with computer executable instructions to perform various computer-implemented operations necessary for timely execution of said allocation, comprising: (a) said computer receiving in its storage and thus having available a list of perishable goods or time-specific resources traded in a given auction round, wherein said list of resources to be traded in said given round is ranked according to factors set by the auctioneer and each resource is traded only in said auction round because said resource loses value if not allocated because it is perishable or time-specific; (b) said computer receiving bids relevant to said auction round wherein each bid comprises a bid price for allocation of one of the resources listed in said list of resources received in step (a), and information identifying a participant bidder making said bid wherein said list of bids is ranked according to bid values; (c) for each of said bid prices received in step (b), said computer: (c1) establishing three classes of bids received in step (b), the highest bids in a Definite Winner class, the lowest bids in a Definite Loser class and the remaining bids in a Possible Winner class, of which only the Possible Winner class must be non-empty; (c2) assigning resources to bids in the Definite Winner class by matching resource to bids with the same rank established in step (a) for resources and step (b) for bids; (c3) assigning the remaining resources in the order of their ranks established in step (a) to bids in the Possible Winner class in the order of their ranks established in step (b) under the condition that they consecutively lost the number of auction rounds k>0, set by the auctioneer, but they sent the same or higher bid for the current auction round; (c4) if any resources are left after step (c3), they are assigned in the order of their ranks from step (a) to bids remaining in the Possible Winner class in the order of their ranks from step (b).
 9. The method of claim 8 wherein an auctioneer sets minimum bid prices for bids that are assigned to the Definite Winner and Possible Winner classes in step (c1).
 10. The method of claim 8 wherein an auctioneer sets a maximum number of bids that can belong to the Definite Winner class and a maximum number of bids that can belong to the Possible Winner class in step (c1).
 11. The method of claim 8 wherein an auctioneer sets the number of consecutive losses defined in step (c3) to one.
 12. The method of claim 8 wherein resources traded in each auction round comprise spaces for paid advertisements on at least one internet page.
 13. A method for an auctioneer to allocate perishable or time-specific resources to bids in a plurality of auction rounds, wherein allocating resources to bids in each auction round is executed on at least one computer comprising computer-readable medium with computer executable instructions to perform various computer-implemented operations necessary for timely execution of said allocation, comprising: (a) said computer receiving in its storage and thus having available a list of perishable goods or time-specific resources traded in a given auction round, wherein said list of resources to be traded in said given round is ranked according to factors set by the auctioneer and each resource is traded only in said auction round because said resource loses value if not allocated because it is perishable or time-specific; (b) said computer receiving bids relevant to said auction round wherein each bid comprises a bid price for allocation of one of the resources listed in said list of resources received in step (a), and information identifying a participant bidder making said bid wherein said list of bids is ranked according to bid values; (c) for each of said bid prices received in step (b), said computer (c1) establishing three classes of bids received in step (b), the highest bids in a Definite Winner class, the lowest bids in a Definite Loser class and the remaining bids in a Possible Winner class, of which only Possible Winner class must to be non-empty; (c2) assigning to bids in the Definite Winner class resources by matching resources to bids with the same rank established in step (a) for resources and step (b) for bids; (c3) computing bid value of each bid in the Possible Winner class in such a way that bid value rewards bids that lost the last action round compared to bids that won the last action round, after which the all bids are ranked according to bid values; (c4) assigning the remaining resources in the order of their ranks established in step (a) to bids in the Possible Winner class in the order of their ranks established in step (c3).
 14. The method of claim 13 wherein an auctioneer sets minimum bid prices for bids that are assigned to Definite Winner and Possible Winner classes in step (c1).
 15. The method of claim 13 wherein an auctioneer sets a maximum number of bids that can belong to Definite Winner class and a maximum number of bids that can belong to Possible Winner class in step (c1).
 16. The method of claim 13 wherein bid value v defined in step (c3) is increased from a bid b by an additive increment a, so v=b+a, but only for the losers of the last auction round but bid value is equal to bid b otherwise.
 17. The method of claim 13 wherein bid value v defined in step (c3) is increased from a bid b by a multiplicative increment m, so v=m*b, for losers of the last auction round, but bid value is equal to bid b otherwise.
 18. The method of claim 13 wherein bid value is a reward for participation in the current and previous auction rounds and is defined as the score WS_(i) defined for each bidder ranked i in Possible Winner class as the difference between the product of k-th power of bid ranked i in step (b) and the number of auction round that it participated in divided by coefficient a and the number of winning rounds, that can be expressed algebraically as WS_(i)=b_(i) ^(k) NP_(i)/α−NW_(i), where NP, and NW, denote the cumulative number of times that bidder ranked i participated and won, respectively, up to and including the current auction round.
 19. The method of claim 13 wherein resources traded in each auction round comprise spaces for paid advertisements on at least one internet page. 